{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# PDE-FIND for identifying Navier-Stokes with added noise\n",
    "\n",
    "Samuel Rudy, 2016\n",
    "\n",
    "This notebook demonstrates PDE-FIND for the vorticity equation given a simulation of fluid flowing around a cylinder with artificial noise added to the solution.\n",
    "\\begin{align*}\n",
    "\\omega_t &= \\frac{1}{Re}\\nabla^2 \\omega - (V \\cdot \\nabla)\\omega\\\\\n",
    "V &= (v,u)\\\\\n",
    "Re &= 100\n",
    "\\end{align*}\n",
    "The x and y components of the velocity field are given as forcing terms to the PDE.  That is, they appear in $\\Theta$, but are not differentiated."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Populating the interactive namespace from numpy and matplotlib\n"
     ]
    }
   ],
   "source": [
    "%pylab inline\n",
    "pylab.rcParams['figure.figsize'] = (12, 6)\n",
    "import numpy as np\n",
    "from mpl_toolkits.mplot3d import Axes3D\n",
    "from PDE_FIND import *\n",
    "import scipy.io as sio\n",
    "import itertools"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "First load the data.  Plotted below is a single timepoint with red outlining the area in which points have been samples for use in the algorithm."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/home/samuel/anaconda3/envs/py27/lib/python2.7/site-packages/ipykernel/__main__.py:35: VisibleDeprecationWarning: using a non-integer number instead of an integer will result in an error in the future\n",
      "/home/samuel/anaconda3/envs/py27/lib/python2.7/site-packages/ipykernel/__main__.py:36: VisibleDeprecationWarning: using a non-integer number instead of an integer will result in an error in the future\n",
      "/home/samuel/anaconda3/envs/py27/lib/python2.7/site-packages/ipykernel/__main__.py:37: VisibleDeprecationWarning: using a non-integer number instead of an integer will result in an error in the future\n"
     ]
    },
    {
     "data": {
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JTpj5XbCz8T2WiL5Nvka2vvljAXw4TuJcwTiuhC3v9gjYyhTxjcq17b9fGY3xswD8+sDm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\nAAAaIKEGAAAAGvg/Z+UTzOScfosAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f1d0b44c2d0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Load data\n",
    "data = sio.loadmat('../CYLINDER/DATA/ALL.mat')\n",
    "steps = 151\n",
    "n = 449\n",
    "m = 199\n",
    "W = data['VORTALL'].reshape(n,m,steps)   # vorticity\n",
    "U = data['UALL'].reshape(n,m,steps)      # x-component of velocity\n",
    "V = data['VALL'].reshape(n,m,steps)      # y-component of velocity\n",
    "\n",
    "dt = 0.2\n",
    "dx = 0.02\n",
    "dy = 0.02\n",
    "\n",
    "# plot the data\n",
    "xx, yy = meshgrid(\n",
    "    np.arange(449)*dx,\n",
    "    np.arange(199)*dy)\n",
    "pcolor(xx,yy,W[:,:,75].T,cmap='coolwarm', vmin=-4, vmax=4)\n",
    "\n",
    "# Cut out the portion of the data before the cylinder\n",
    "xmin = 100*dx\n",
    "xmax = 425*dx\n",
    "ymin = 15*dy\n",
    "ymax = 185*dy\n",
    "plot([xmin,xmin],[ymin,ymax],'r',linewidth = 2)\n",
    "plot([xmax,xmax],[ymin,ymax],'r',linewidth = 2)\n",
    "plot([xmin,xmax],[ymin,ymin],'r',linewidth = 2)\n",
    "plot([xmin,xmax],[ymax,ymax],'r',linewidth = 2)\n",
    "xlim([0,n*dx-dx])\n",
    "ylim([0,m*dy])\n",
    "title('Sampling Region for Navier Stokes', fontsize = 20)\n",
    "xlabel('x', fontsize = 16)\n",
    "ylabel('y', fontsize = 16)\n",
    "\n",
    "W = W[xmin:xmax,ymin:ymax,:]\n",
    "U = U[xmin:xmax,ymin:ymax,:]\n",
    "V = V[xmin:xmax,ymin:ymax,:]\n",
    "n,m,steps = W.shape\n",
    "\n",
    "# Add in noise with magnitude equal to 1% of std dev of data\n",
    "numpy.random.seed(0)\n",
    "Wn = W + 0.01*np.std(W)*np.random.randn(n,m,steps)\n",
    "Un = U + 0.01*np.std(U)*np.random.randn(n,m,steps)\n",
    "Vn = V + 0.01*np.std(V)*np.random.randn(n,m,steps)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Denoising using the SVD\n",
    "\n",
    "Now denoise using the SVD.  Each snapshot in time is arranged into a column and the resulting matrix is projected onto a low dimensional subspace given by it's most dominant singular vectors.  The dimension used is determined visually from looking for a Pareto front on the singular values, which is easy to see in their plot.  Notice that compared to the clean data, the noisy data's singular values do not fall below a certain value.  We consider those lying on this flat line to correspond to the artificial noise, and throw them away."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "W = W.reshape(n*m,steps)\n",
    "U = U.reshape(n*m,steps)\n",
    "V = V.reshape(n*m,steps)\n",
    "\n",
    "Wn = Wn.reshape(n*m,steps)\n",
    "Un = Un.reshape(n*m,steps)\n",
    "Vn = Vn.reshape(n*m,steps)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "uw,sigmaw,vw = svd(W, full_matrices=False); vw = vw.T\n",
    "uu,sigmau,vu = svd(U, full_matrices=False); vu = vu.T\n",
    "uv,sigmav,vv = svd(V, full_matrices=False); vv = vv.T\n",
    "\n",
    "uwn,sigmawn,vwn = svd(Wn, full_matrices=False); vwn = vwn.T\n",
    "uun,sigmaun,vun = svd(Un, full_matrices=False); vun = vun.T\n",
    "uvn,sigmavn,vvn = svd(Vn, full_matrices=False); vvn = vvn.T"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.text.Text at 0x7f8bfcff0a50>"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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odqHSicEjisOf0o05G39gPR9/ut2AjWY2An+Kd0UptS3Zj43YvpRsBJWl+N7WOvjtGfNL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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f8bfd0128d0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# singular values of clean data\n",
    "semilogy(np.arange(151),sigmaw, 'r', label = r'$\\omega$')\n",
    "semilogy(np.arange(151),sigmau, 'g', label = r'$u$')\n",
    "semilogy(np.arange(151),sigmav, 'b', label = r'$v$')\n",
    "\n",
    "# singular values of noisy data\n",
    "semilogy(np.arange(151),sigmawn, '--',color ='r')\n",
    "semilogy(np.arange(151),sigmaun, '--',color ='g')\n",
    "semilogy(np.arange(151),sigmavn, '--',color ='b')\n",
    "\n",
    "legend(loc = 'upper right', fontsize = 20)\n",
    "xticks(fontsize = 16)\n",
    "yticks(fontsize = 16)\n",
    "\n",
    "title('Singular Values from Proper Orthogonal Decomposition\\n (Dashed with noise)', fontsize = 20)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "dim_w = 26\n",
    "dim_u = 20\n",
    "dim_v = 20\n",
    "\n",
    "Wn = uwn[:,0:dim_w].dot(np.diag(sigmawn[0:dim_w]).dot(vwn[:,0:dim_w].T)).reshape(n,m,steps)\n",
    "Un = uun[:,0:dim_u].dot(np.diag(sigmaun[0:dim_u]).dot(vun[:,0:dim_u].T)).reshape(n,m,steps)\n",
    "Vn = uvn[:,0:dim_v].dot(np.diag(sigmavn[0:dim_v]).dot(vvn[:,0:dim_v].T)).reshape(n,m,steps)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Sample data points\n",
    "\n",
    "Now collect a sample of points to use for PDE-FIND.  Here we take 5000 spatial points and 60 time points at each."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "# Sample a collection of data points, stay away from edges so I can just use centered finite differences.\n",
    "num_xy = 5000\n",
    "num_t = 60\n",
    "num_points = num_xy * num_t\n",
    "boundary = 5\n",
    "boundary_x = 10\n",
    "points = {}\n",
    "count = 0\n",
    "\n",
    "for p in range(num_xy):\n",
    "    x = np.random.choice(np.arange(boundary_x,n-boundary_x),1)[0]\n",
    "    y = np.random.choice(np.arange(boundary,m-boundary),1)[0]\n",
    "    for t in range(num_t):\n",
    "        points[count] = [x,y,2*t+12]\n",
    "        count = count + 1"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Construct $\\Theta (U)$ and compute $U_t$\n",
    "\n",
    "Take derivatives and assemble into $\\Theta(\\omega, u ,v)$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "# Take derivatives of vorticity at each point.  Not the most elegant way of doing this...\n",
    "#PolyDiffPoint(array of fcn vals, domain vals, degree, derivatives to take): -> array of derivatives  \n",
    "\n",
    "# Take up to second order derivatives.\n",
    "w = np.zeros((num_points,1))\n",
    "u = np.zeros((num_points,1))\n",
    "v = np.zeros((num_points,1))\n",
    "wt = np.zeros((num_points,1))\n",
    "wx = np.zeros((num_points,1))\n",
    "wy = np.zeros((num_points,1))\n",
    "wxx = np.zeros((num_points,1))\n",
    "wxy = np.zeros((num_points,1))\n",
    "wyy = np.zeros((num_points,1))\n",
    "\n",
    "N = 2*boundary-1  # odd number of points to use in fitting\n",
    "Nx = 2*boundary_x-1  # odd number of points to use in fitting\n",
    "deg = 5 # degree of polynomial to use\n",
    "\n",
    "for p in points.keys():\n",
    "    \n",
    "    [x,y,t] = points[p]\n",
    "    w[p] = Wn[x,y,t]\n",
    "    u[p] = Un[x,y,t]\n",
    "    v[p] = Vn[x,y,t]\n",
    "    \n",
    "    wt[p] = PolyDiffPoint(Wn[x,y,t-(N-1)/2:t+(N+1)/2], np.arange(N)*dt, deg, 1)[0]\n",
    "    \n",
    "    x_diff = PolyDiffPoint(Wn[x-(Nx-1)/2:x+(Nx+1)/2,y,t], np.arange(Nx)*dx, deg, 2)\n",
    "    y_diff = PolyDiffPoint(Wn[x,y-(N-1)/2:y+(N+1)/2,t], np.arange(N)*dy, deg, 2)\n",
    "    wx[p] = x_diff[0]\n",
    "    wy[p] = y_diff[0]\n",
    "    \n",
    "    x_diff_yp = PolyDiffPoint(Wn[x-(Nx-1)/2:x+(Nx+1)/2,y+1,t], np.arange(Nx)*dx, deg, 2)\n",
    "    x_diff_ym = PolyDiffPoint(Wn[x-(Nx-1)/2:x+(Nx+1)/2,y-1,t], np.arange(Nx)*dx, deg, 2)\n",
    "    \n",
    "    wxx[p] = x_diff[1]\n",
    "    wxy[p] = (x_diff_yp[0]-x_diff_ym[0])/(2*dy)\n",
    "    wyy[p] = y_diff[1]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "# Form a huge matrix using up to quadratic polynomials in all variables.\n",
    "X_data = np.hstack([w,u,v])\n",
    "X_ders = np.hstack([np.ones((num_points,1)), wx, wy, wxx, wxy, wyy])\n",
    "X_ders_descr = ['','w_{x}', 'w_{y}','w_{xx}','w_{xy}','w_{yy}']\n",
    "X, description = build_Theta(X_data, X_ders, X_ders_descr, 2, data_description = ['w','u','v'])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "These are all the cadidate functions which we are selecting from."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "['',\n",
       " 'w_{x}',\n",
       " 'w_{y}',\n",
       " 'w_{xx}',\n",
       " 'w_{xy}',\n",
       " 'w_{yy}',\n",
       " 'uv',\n",
       " 'v^2',\n",
       " 'u^2',\n",
       " 'w',\n",
       " 'wu',\n",
       " 'v',\n",
       " 'wv',\n",
       " 'u',\n",
       " 'w^2',\n",
       " 'uvw_{x}',\n",
       " 'v^2w_{x}',\n",
       " 'u^2w_{x}',\n",
       " 'ww_{x}',\n",
       " 'wuw_{x}',\n",
       " 'vw_{x}',\n",
       " 'wvw_{x}',\n",
       " 'uw_{x}',\n",
       " 'w^2w_{x}',\n",
       " 'uvw_{y}',\n",
       " 'v^2w_{y}',\n",
       " 'u^2w_{y}',\n",
       " 'ww_{y}',\n",
       " 'wuw_{y}',\n",
       " 'vw_{y}',\n",
       " 'wvw_{y}',\n",
       " 'uw_{y}',\n",
       " 'w^2w_{y}',\n",
       " 'uvw_{xx}',\n",
       " 'v^2w_{xx}',\n",
       " 'u^2w_{xx}',\n",
       " 'ww_{xx}',\n",
       " 'wuw_{xx}',\n",
       " 'vw_{xx}',\n",
       " 'wvw_{xx}',\n",
       " 'uw_{xx}',\n",
       " 'w^2w_{xx}',\n",
       " 'uvw_{xy}',\n",
       " 'v^2w_{xy}',\n",
       " 'u^2w_{xy}',\n",
       " 'ww_{xy}',\n",
       " 'wuw_{xy}',\n",
       " 'vw_{xy}',\n",
       " 'wvw_{xy}',\n",
       " 'uw_{xy}',\n",
       " 'w^2w_{xy}',\n",
       " 'uvw_{yy}',\n",
       " 'v^2w_{yy}',\n",
       " 'u^2w_{yy}',\n",
       " 'ww_{yy}',\n",
       " 'wuw_{yy}',\n",
       " 'vw_{yy}',\n",
       " 'wvw_{yy}',\n",
       " 'uw_{yy}',\n",
       " 'w^2w_{yy}']"
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "description"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Solve for $\\xi$\n",
    "\n",
    "TrainSTRidge splits the data up into 80% for training and 20% for validation.  It searches over various tolerances in the STRidge algorithm and finds the one with the best performance on the validation set, including an $\\ell^0$ penalty for $\\xi$ in the loss function."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "w_t = (0.010707 +0.000000i)w_{xx}\n",
      "    + (0.008346 +0.000000i)w_{yy}\n",
      "    + (-0.987655 +0.000000i)uw_{x}\n",
      "    + (-0.982926 +0.000000i)vw_{y}\n",
      "   \n"
     ]
    }
   ],
   "source": [
    "lam = 10**-5\n",
    "d_tol = 5\n",
    "c = TrainSTRidge(X,wt,lam,d_tol)\n",
    "print_pde(c, description, ut = 'w_t')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.7945\n",
      "0.697610145425\n"
     ]
    }
   ],
   "source": [
    "err = abs(np.array([0.010707-0.01, 0.008346-0.01, -0.987655+1, -0.982926+1]))\n",
    "print mean(err)*100\n",
    "print std(err)*100"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": []
  }
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